Famitsu.com managed to get some new screens of Persona 4 Arena's home conversion. Included in the handful of shots is the game's mode select screen:

The screen shows the following options:

Lesson Mode

Story Mode

Arcade mode

Score Attack Mode

Training Mode

Challenge Mode

Versus Mode

Network Mode

Contents Market

Replay Theater

Gallery Mode

Option

The site does not have details on the modes, but you can probably figure out what most of them are based off the name.

The other screens show scenes from the story mode. When you start off the game, you'll have access to four characters: the main character, Chie, Yosuke and Yukiko. Other characters will be unlocked as you play. The main character's story begins with a reunion with his friends and family.